Question

Find the diameter of a sphere whose surface area is 616 cm square

Answer 1

Answer:

→ Diameter = 14 cm

Step-by-step explanation:

→ Surface area = 4πr²

616 = 4πr²

4πr² = 616

2×2× 3.14 × r² = 616

${r}^{2} = \frac{616}{4 \times 3.14} \\ \\ {r}^{2} = 49 cm$

r = 7 cm

→ Diameter = 2 × r

→ Diameter = 2 × 7

→ Diameter = 14 cm

Answer 2

Diameter of the sphere is 14 cm whose surface area is 616 cm square

Given:

• A sphere with surface area 616 cm²

To Find:

• Radius of the sphere

Solution:

• Surface area of sphere = 4πR²   where R is the radius
• Approximate value of pi is taken as 3.14  or 22/7
• Diamter = 2 x Radius

Step 1:

Assume that Radius of sphere is R cm Hence find Surface area of the sphere

Surface Area of sphere = 4πR²    cm²

Step 2:

Use π = 22/7  and Equate Surface area to given 616 cm²

4 (22/7) R² = 616

Step 3:

Solve for R

4 (22/7) R² = 616

(22/7) R² = 154  ( Divide both sides by 4)

(1/7) R² = 7    ( Divide both sides by 22)

R² = 7 x 7   ( Multiply both sides by 7)

R² = 7²

=> R = 7     ( Taking Square root both sides)

Step 4:

Use Diameter = 2 x Radius and substitute radius = 7

Diameter = 2 x 7 = 14 cm

Hence Diameter =14 cm